| Eberlein mulian定理在局部凸空间中的推广 |
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| 引用本文： | 武俊德,李容录,曲文波.Eberlein mulian定理在局部凸空间中的推广[J].数学学报,1998,41(3). |
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| 作者姓名： | 武俊德 李容录 曲文波 |
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| 作者单位： | 大庆石油学院数学系(武俊德)，哈尔滨工业大学数学系(李容录)，大庆高专数学系(曲文波) |
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| 摘 要： | 设（Ｅ，Ｔ）是一个分离的局部凸空间．本文主要结果是：（１）如果（Ｅ，Ｔ）是次可分的，那么ＡＥ是相对弱紧集Ａ是相对弱可数紧集Ａ是相对弱序列紧集．（２）如果（Ｅ，Ｔ）是强次可分且（Ｅ，β（Ｅ，Ｅ））是桶型空间，那么ＡＥ是相对弱紧集Ａ是相对弱可数紧集Ａ是相对弱序列紧集．
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| 关 键 词： | 相对弱紧，相对弱可数紧，相对弱序列紧，Eberlein-mulian定理 |
| 收稿时间： | 1996-4-12 |
The Extension of Eberlein Sˇmulian Theorem in Locally Convex Spaces |
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| Wu Junde.The Extension of Eberlein Sˇmulian Theorem in Locally Convex Spaces[J].Acta Mathematica Sinica,1998,41(3). |
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| Authors: | Wu Junde |
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| Institution: | Wu Junde ( Department of Mathematics, Daqing Petroleum Institute, Anda 151400 , China ) Li Ronglu ( Department of Mathematics, Harbin Institute of Technology, Harbin 150006 , China ) Qu Wenbo ( Department of Mathematics, D |
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| Abstract: | Let (E,T) be a separated locally convex space. The main results obtained in this paper are:(1) If (E,T) is sub separable, then AE is a relatively weakly compact set A is a relatively weakly countable compact set A is a relatively weakly sequentially compact set. (2) If (E,T) is strongly sub separable and (E *, β(E *,E)) is a barrelled space, then AE is a relatively weakly compact set A is a relatively weakly countable compact set A is a relatively weakly sequentially compact set. |
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| Keywords: | Relatively weakly compact Relatively weakly countable compact Relatively weakly sequentially compact Eberlein Sˇmulian theorem |
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